Theorem velpw

Description: Setvar variable membership in a power class. (Contributed by David A. Wheeler, 8-Dec-2018)

	Ref	Expression
Assertion	velpw	$$⊢x\in 𝒫A\leftrightarrow x\subseteq A$$

Proof

Step	Hyp	Ref	Expression
1		vex	$$⊢x\in \mathrm{V}$$
2	1	elpw	$$⊢x\in 𝒫A\leftrightarrow x\subseteq A$$